The Obamas turn up in Paris this evening, but have declined a dinner invitation from the couple next door: the Sarkozys.

President Obama’s reluctance to spend more than minimum time with the French leader on his visit for the D-Day anniversary has come as an embarrassment to the Elysée Palace.

America’s First Family will not be dining with President Sarkozy and his wife, Carla Bruni, even though they are staying at the residence of the US Ambassador, yards from the Elysée apartments where the Sarkozys spend their weekends.

Mr Sarkozy’s staff were trying yesterday to arrange another private moment between the couples. Mr Obama is due to fly back to Washington tomorrow night or on Sunday.

Mr Sarkozy’s dream date would be dinner somewhere spectacular such as the Jules Verne, an Alain Ducasse restaurant on the Eiffel Tower. The Obamas were reported on French celebrity websites to be planning a meal there.

A glamorous joint outing might be compared with the ones that President de Gaulle undertook with John and Jackie Kennedy in 1961. On that trip, Mrs Kennedy was such a hit that JFK presented himself as “the man who accompanied Jackie Kennedy to Paris”.

Failure to socialise with the Obamas will add to mockery that has greeted Mr Sarkozy’s attempts to stage the 65th anniversary of D-Day as a “Barack and Sarko show”. The media and Opposition have mocked Mr Sarkozy over Mr Obama’s coolness towards him, which is only partly due to his handling of the Normandy commemoration.

Mr Sarkozy has been pilloried in France for his failure to invite the Queen to the events. “The palace is fearing a snub,” Le Parisien newspaper said yesterday after the news emerged of the Obamas’ plans to keep themselves to themselves.

Yesterday the popular comedian Nicolas Canteloup did an impression of Mr Sarkozy worrying that he had “only two days to become tall, handsome and elegant”. The French leader is 5½ inches shorter than Michelle Obama.

The French were also piqued after the White House said that it was working on an invitation to Normandy for the Royal Family. Face was saved when the Prince of Wales agreed to attend with Gordon Brown. “Sarkozy has pulled off a double hit: insulting Queen Elizabeth and exasperating Obama,” the weekly Canard Enchaîné said on Wednesday.

French worries about being snubbed were matched in Germany, where media and politicians are convinced that the brevity of Mr Obama’s trip there and a decision to avoid Berlin demonstrated his disapproval of Angela Merkel, the Chancellor. Mr Obama was due in Germany last night for a visit to Dresden and the Buchenwald death camp.

Mr Obama’s irritation with his French counterpart began when Mr Sarkozy tried to grab the limelight at the G20 summit in London in April and talked condescendingly of the US President in private. Mr Sarkozy told colleagues that he found Mr Obama to be inexperienced and unbriefed, especially on climate change. Mr Obama hit back last month, telling a visiting French minister: “Please tell Nicolas that I shall do my homework, and in two months I’ll know all about climate change.”

The leaders will have lunch in Caen tomorrow while their wives meet near by. They will then all attend the ceremony at the US cemetery at Colleville-sur-Mer, above Omaha Beach.

Philippe Duron, the Mayor of Caen, has minted a slogan for his town in honour of Mr Obama: “Yes we Caen!”